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Electromagnetic parameter retrieval from inhomogeneous metamaterials

D. R. Smith, D. C. Vier, Th. Koschny, and C. M. Soukoulis
Phys. Rev. E 71, 036617 – Published 22 March 2005
An article within the collection: Physical Review E 25th Anniversary Milestones

Abstract

We discuss the validity of standard retrieval methods that assign bulk electromagnetic properties, such as the electric permittivity ε and the magnetic permeability μ, from calculations of the scattering (S) parameters for finite-thickness samples. S-parameter retrieval methods have recently become the principal means of characterizing artificially structured metamaterials, which, by nature, are inherently inhomogeneous. While the unit cell of a metamaterial can be made considerably smaller than the free space wavelength, there remains a significant variation of the phase across the unit cell at operational frequencies in nearly all metamaterial structures reported to date. In this respect, metamaterials do not rigorously satisfy an effective medium limit and are closer conceptually to photonic crystals. Nevertheless, we show here that a modification of the standard S-parameter retrieval procedure yields physically reasonable values for the retrieved electromagnetic parameters, even when there is significant inhomogeneity within the unit cell of the structure. We thus distinguish a metamaterial regime, as opposed to the effective medium or photonic crystal regimes, in which a refractive index can be rigorously established but where the wave impedance can only be approximately defined. We present numerical simulations on typical metamaterial structures to illustrate the modified retrieval algorithm and the impact on the retrieved material parameters. We find that no changes to the standard retrieval procedures are necessary when the inhomogeneous unit cell is symmetric along the propagation axis; however, when the unit cell does not possess this symmetry, a modified procedure—in which a periodic structure is assumed—is required to obtain meaningful electromagnetic material parameters.

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  • Received 21 November 2004

DOI:https://doi.org/10.1103/PhysRevE.71.036617

©2005 American Physical Society

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This article appears in the following collection:

Physical Review E 25th Anniversary Milestones

The year 2018 marks the 25th anniversary of Physical Review E. To celebrate the journal’s rich legacy, during the upcoming year we highlight a series of papers that made important contributions to their field. These milestone articles were nominated by members of the Editorial Board of Physical Review E, in collaboration with the journal’s editors. The 25 milestone articles, including an article for each calendar year from 1993 through 2017 and spanning all major subject areas of the journal, will be unveiled in chronological order and will be featured on the journal website.

Authors & Affiliations

D. R. Smith1,2,*, D. C. Vier2, Th. Koschny3,4, and C. M. Soukoulis3,4

  • 1Department of Electrical and Computer Engineering, Duke University, Box 90291, Durham, North Carolina 27708, USA
  • 2Department of Physics, University of California, San Diego, La Jolla, California 92093, USA
  • 3Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
  • 4Foundation for Research and Technology Hellas (FORTH), 71110 Heraklion, Crete, Greece

  • *Email address: drsmith@ee.duke.edu

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Issue

Vol. 71, Iss. 3 — March 2005

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